Surface observation data were obtained from the China National Environmental Monitoring Center (CNEMC; data available at http://www.pm25.in, last access: 25 June 2021). Hourly ambient air concentration data for PM10, PM2.5, CO, NO2, O3, and SO2 were available for 1571 sites (over China) and 1459 sites (within the study domain; Fig. 1). After removing sites with less than 80 % data availability for each year (2017–2020, ± 60 d of Lunar New Year (LNY)), the analysis used observations from 1332 sites. Data-processing procedures are explained in Sect. 3.1 and further discussed in Sect. 4.4.

The TROPOspheric Monitoring Instrument (TROPOMI) NO2 vertical column-density, level-2 data (S5P_L2_NO2) were obtained from NASA GES DISC (http://tropomi.gesdisc.eosdis.nasa.gov, last access: 25 June 2021). TROPOMI is a hyperspectral spectrometer onboard the Sentinel-5P satellite, with wavelength coverage over ultraviolet to visible (270 to 495 nm), near infrared (675–775 nm), and shortwave infrared (2305–2385 nm) wavelengths (Eskes et al., 2019; van Geffen et al., 2019). High-quality pixels from level-2 data (3.5 km × 7 km resolution at the nadir) were selected using the quality flags provided by the product (qa_value > 0.75) and then spatially regridded into the study domain using a conservative spatial-regridding method that preserves mass during interpolation (Kim et al., 2018, 2016, 2020).

Meteorological and atmospheric chemistry transport models were used over East Asia with a 27 km horizontal resolution. The Weather Research and Forecasting Model (WRF, version 3.4.1) was used for meteorological simulations (Skamarock and Klemp, 2008). The National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Protection (NCEP) Final Analysis (FNL) product (NCEP, 2000) provided the initial and boundary conditions for the WRF simulations. For chemistry simulations, CMAQ (version 4.7.1) (Byun and Schere, 2006), the Meteorology–Chemistry Interface Processor (MCIP, version 3.6) (Otte and Pleim, 2010), and the Sparse Matrix Operator Kernel Emission (SMOKE) modeling framework were used, employing the meteorological inputs provided by the WRF simulations. Table 1 details the modeling configurations, and Fig. S1 in the Supplement compares models with observations. The models provide a reasonably realistic simulation of atmospheric chemical and physical processes over the considered domain, especially in terms of their daily variations from 2017 to 2019 (e.g., R = 0.91 ∼ 0.94 for PM2.5, see Emery et al. (2017) for general model performance guidance). However, in 2020, as the effects of the pandemic began to take hold, the chemical model's predictions – based on typical (as opposed to pandemic-influenced) emissions – systematically overpredicted pollutant concentrations, consistent with a pandemic-influenced reduction in emissions.

This study used two sets of emission inventories, the Comprehensive Regional emission inventory for Atmospheric Transport Experiment (CREATE, version 2.3) (Jang et al., 2020) and the Model Inter-Comparison Study for Asia (MICS-Asia) emission inventory (MIX inventory for the year 2010) (Li et al., 2017). While the CREATE inventory is based on the latest information, including the 2016 KORUS-AQ campaign (https://espo.nasa.gov/korus-aq, last access: 25 June 2021), the MIX inventory has been tested in many diverse applications (J. Li et al., 2019; K. Li et al., 2019; Zhang et al., 2017). The time-series analysis in Fig. 2 (discussed below) was based on the CREATE emission inventory, but the results of the analysis did not depend in any significant way on a choice between these two base inventories. The CREATE inventory is provided as an annual mean for each Chinese province for the year 2016 and the SMOKE preprocessor was used to convert the inventory to hourly model-ready inputs. The base model simulations use these 2016 emissions for the entire 2017–2020 modeling period.

Four types of variation (meteorological, weekly, yearly, and the Chinese spring festival) were reduced or accounted for in the surface observations, as follows. Meteorological influences were reduced by combining surface data with output from a three-dimensional chemistry model to calculate estimated emissions. Since the model simulations with a fixed emission inventory respond to the variations in meteorological conditions, we can infer the relationship between emissions and ambient pollutant concentrations under specific weather conditions. By applying this relationship, we convert the changes in observed concentrations into the changes in emissions. Weekly variations, a unique feature of anthropogenic emissions, were removed by using a 7 d moving average. The impact of the Chinese spring festival, the biggest traditional holiday celebrating Lunar New Year (LNY), was normalized by rearranging the time series to center on the LNY in each solar year. The LNY alignment was necessary to account for the irregular occurrence of the LNY dates. Seven-day moving average filtering was also required to avoid unfair comparisons between different weekdays after the LNY alignment. Otherwise, we may compare different weekdays for different year (e.g., 2020 LNY on 25 January, Saturday, and 2019 LNY is February 5, Tuesday). Figure S4 shows that the 7 d moving average filter smooths but does not significantly change the time-series results. Finally, yearly emission variations were removed by setting a base period (-60 to -10 d before LNY) and calculating relative changes from the average of the base period.

We followed the data-processing procedures suggested by Bae et al. (2020b) for their emissions-updating system (hereafter BAE2020). First, the observational and modeled data were paired and tested, and observation sites with more than 20 % of values missing were discarded. To avoid over-weighting dense urban sites, observations occurring within the same model grid cell were averaged. Second, weekly variations were removed using 7 d moving averages, and the impact of the Chinese spring festival was normalized by rearranging the time series to center on LNY in each year. Third, meteorological variations were removed by applying the ratio between observed and modeled concentrations. Using a simple linear assumption, observed pollutant concentrations were combined with the results of the chemical model to create estimates of actual emissions that are less sensitive to meteorological variations. Use of the linear assumption in the concentration-to-emission conversion is further discussed in Sect. 4.4 The total estimated emissions, Eest, and their relative variations, rEest, were calculated as 1Eest(t)=Emod⋅Cobs(t)Cmod(t),2rEest(t)=Eest(t)∑t=baseEest(t)/nbase⋅100%, where C is the daily pollutant concentration; t is days from LNY; base and nbase are the pre-LNY base period (shown in Fig. 2) and its number of days, respectively; and Emod is the model emissions. To normalize the yearly changes, a base period (-60 to -10 d before LNY) was set, with relative changes calculated from the average of that base period (i.e., rEest(t)). The impact of the pandemic was inferred by calculating the difference in estimated emissions between normal years and 2020. Since the model uses a fixed emission inventory for each year, Emod cancels out in the comparison.

For the spatial analyses of the data (e.g., Fig. 3), point data were converted to area format. Similar to the time-series data processing, the observational and modeled data were paired and tested. Considering the location of each paired data set, we assigned point data to their corresponding Chinese prefecture. By averaging all concentrations in each prefecture, we constructed the prefecture-level concentration data set (for each prefecture polygon), which was then converted into domain grids using a conservative spatial-regridding technique. Section 4.4 further discusses the data-processing procedures.

For the second analysis (discussed in Sect. 4.2), we updated major pollutant emissions to a more realistic level and analyzed simulated chemical behaviors. Due to stringent emission control policies by the Chinese government, Chinese anthropogenic emissions have changed dramatically over recent years. For example, the annual mean surface SO2 concentration across China was 8.4 ppb in 2016 but dropped to less than half of this level (3.7 ppb) in 2020. To incorporate a realistic change in emissions from 2016 to 2020, we applied observation-based emission adjustment factors to the 2016 CREATE emission inventory to reproduce emissions in 2020. In general, model emissions can be adjusted based on the ratios between observed and modeled surface concentrations: 3EadjEmod=β⋅CobsCmod, where β is a sensitivity factor in the emission-to-concentration conversion. β is close to 1 if less secondary chemical reactions are involved. BAE2020 assumed a fixed β=1 to update SO2 emissions, and they demonstrated that the adjusted emissions effectively reproduced surface SO2 concentrations over China. Similar approaches were also confirmed to be effective for the NOx emission adjustment over the same East Asian domain using satellite-based measurements of NO2 column densities (Bae et al., 2020a; Chang et al., 2016).

While this simple assumption works practically, we tried to conduct the emission adjustment processing more carefully, considering the unprecedented changes in the chemical environment during the pandemic period. We extend the approach of BAE2020, offering two major enhancements. First, we calculate daily emission adjustment factors to represent the rapid changes in emissions under the pandemic situation. We applied 14 d moving averages to avoid uncertainties caused by insufficient data points day to day. Second, we calculated spatial and temporal variations in β and then applied these to the emission adjustment factors. Table 2 compares the data-processing steps used in this study with those used in BAE2020.

The β values are calculated as follows. In the real world, the sensitivity of concentration to changes in emissions is not unique or spatially homogeneous (i.e., β≠1), especially for NOx emissions and NO2 concentrations. β values for specific location and time can be calculated if we have two model simulations with different emissions applied. Previous studies have calculated β values for a model by using changes in concentration caused by a certain amount of perturbed emissions (e.g., Lamsal et al., 2011, used a 15 % emission perturbation).

To obtain more realistic β values, we have conducted two model simulations: base and adj1 runs. First, the base model simulation was conducted using a normal emission inventory, CREATE, which we have introduced previously. The second simulation, adj1 run, was conducted using perturbed emissions to estimate how the model responds according to the change in emissions. We adjusted emissions according to the ratio between observed and modeled surface concentrations, so we can reproduce a more realistic chemical environment.

From these two simulations, the base and adj1 runs, we calculate the emissions-to-concentration sensitivity, β values, on a specific spatial and temporal scale – for each Chinese prefecture daily. β values are calculated as 4βp,t=[Eadj1/Ebase]p,t[Cadj1/Cbase]p,t, where p and t stand for indices of Chinese prefectures and specific dates. Using calculated β values for each prefecture and date, we finally obtain the adjusted emissions for the second and final simulations: the adj2 run. 5[Eadj2]p,t=βp,t⋅CobsCbase⋅Ebasep,t

We further discuss the characteristics of the emissions-to-concentration sensitivity in Sect. 4.4.2.

The contributions of emissions from each sector to surface PM2.5 concentrations over China were estimated using the brute-force method (BFM), an approach that uses changes in modeled outputs as a result of perturbed emission inputs (Burr and Zhang, 2011). The MIX emission inventory provides information on five sectors: residential, industry, power generation, transportation, and agriculture. Sectoral contributions were calculated by applying the perturbed emissions for each sector: 6Contr.(sector)=(Cbase-CΔE,sector)/ΔECbase⋅100%, where C is the surface PM2.5 concentration and ΔE is the ratio of the emission perturbations. A 50 % reduction was chosen to perturb emissions for each individual sector. Fractional contributions of each emission sector were calculated compared to the sum of all five emission sector contributions. The application of the BFM to East Asian air quality models and a discussion of its uncertainties has been presented elsewhere (Kim et al., 2017b).

Reducing meteorological, weekly, and yearly variations, as well as variations resulting from the Chinese spring festival made the comparison of pandemic-influenced surface observations to normal conditions more robust and useful. Estimated NOx emissions (Fig. 2) display variations from the spring festival season. From 2017–2019, the estimated NOx emissions demonstrate a clear reduction during the festival period (by up to 45 % between -10 and +20 d from LNY). In 2020, this reduction is slightly greater and continues for longer, implying that the coronavirus outbreak further reduced traffic in China. The difference between the estimated emissions in the 2017–2019 time series and those in the 2020 time series in Fig. 2 reflects the relative significance of the impact of the coronavirus (p < 0.01 for t test of comparison after LNY).

Interestingly, the 2020 time series (that is, the combined effect of the spring festival and the coronavirus) remains flat from the LNY to 15 February. As both effects likely overlapped, they appear inseparable during the period. The maximum impact from the coronavirus seen in the data is a 58 % reduction on 15 February 2020 from the level seen in prior, baseline years (2017–2019). The level of NOx emissions from 1 to 15 February (close to a 50 % reduction) might suggest a floor level for reduced emissions under current conditions in terms of technology and infrastructure. This might have important implications for chemical modeling and emission control, perhaps implying a floor for emission reductions that China can realistically reach under current conditions. The blue line represents a time series from Hubei only (46 sites), showing, as would be expected, that the impact in Hubei has been more significant and sustained.

The reduced NOx emissions began to increase after 15 February, almost recovering to their normal level by the end of March 2020. Hence, the impact of the coronavirus pandemic on NOx emissions in China lasted almost 2 months. Figure 3 shows the spatial distribution of the estimated changes in NOx emissions from the base period to the period of maximum impact (25 January–14 February 2020) and the recovery period (24 February – 15 March 2020). Just after LNY, NOx emissions strongly reduce across China, but their inferred recovery is spatially inhomogeneous. As shown in Fig. 3, Hubei Province continued to show a strong reduction (by more than 50 %) compared with the pre-LNY level, even in the recovery phase (period 2). Other regions show various patterns in NOx levels compared with previous years. These observations are consistent with space-borne, remote-sensing measurements from the TROPOMI (Fig. S1). Similar to the surface observations in Fig. 3, the spatial distributions of NO2 column densities during the period of maximum impact (25 January–14 February) and the recovery period (24 February – 15 March) were generated as changes from the baseline period (26 November 2019–15 January 2020).

The impact of the virus may actually have begun before the spring festival. In normal years (2017–2019), variation in estimated pre-LNY baseline period (-60 to -10 d) NOx emissions is relatively small because the model uses fixed emissions and weekly variations have already been removed. However, the estimated emissions in 2020 are relatively low, starting from about 15 d before LNY, and this relative reduction is more pronounced in Hubei. This suggests that our baseline period in 2020 already includes a partial coronavirus impact. If this is true, the impact of the pandemic would be even stronger than inferred here, as it is based on a year-by-year comparison of concentrations during and after the typical-year base period.

Unlike the temporal trend in NOx emissions and their spatial distribution, a comparison of changes in the PM2.5 level suggests a different story (Fig. 2b). Contrary to NOx emissions, PM2.5 concentrations typically show a slight increase near LNY, likely due to increased PM2.5 emissions from fireworks, a long-held tradition in China (Kong et al., 2015), and show only a relatively moderate reduction from typical levels (by 10 %–20 %) over the remainder of the spring festival. Unlike NOx emissions, the case of PM2.5 involves both direct emissions of particulate matter and gas-to-particle conversion of emitted precursors (e.g., SO2, NOx, NH3, VOCs – volatile organic compounds) mediated by atmospheric chemical transformations. As discussed in the Method section, we assume the same approximate relationship for PM2.5 as with NOx between the ambient observations and their associated emissions. This approach suggests that emissions decreased by roughly 30 % from normal levels through the end of March to reach 72.7 ± 6.6 % of the 2017–2019 level from 4 February to 25 March 2020. Interestingly, the pandemic does not seem to have significantly affected SO2 emissions (see Fig. S3), suggesting that the pandemic's effects on the power generation and industrial sectors have been relatively small.

As discussed in Sect. 3.2 above, we used an alternative approach to investigate unidentified PM2.5 emissions, specifically applying more realistic SO2 and NOx emission adjustments. Using this methodology, we repeated CMAQ simulations with SO2 and NOx emissions adjusted based on surface measurements. Daily and prefecture-level emission-adjustment factors were calculated and applied to the baseline emission inventory. The two CMAQ simulations – a baseline simulation with the CREATE emission inventory and an adjustment simulation with updated emissions – were both compared with observations from surface-monitoring sites (Fig. 4). Individual site comparisons are also available in Fig. S11.

For both SO2 and NO2 concentrations, the CMAQ simulation with adjusted emissions performed well, reproducing observed variations in surface concentrations. It should be noted that the CREATE v2.3 emission inventory we used was constructed for 2016 and applied to a 2020 simulation. Before LNY, simulated NO2 concentrations with both the baseline and adjusted emission inventory agreed well with observations, implying that there were no significant changes in the NOx emission level between 2016 and 2020. Near LNY, the baseline NO2 simulations differ significantly from observations, while the simulation with adjusted emissions successfully reproduced the huge reductions in the LNY and pandemic period. The difference between the baseline and adjusted simulations almost disappears at the end of March, consistent with the result of the time-series analysis (Fig. 2). On the other hand, the baseline SO2 simulations greatly overestimate observations by 2 or 3 times, implying that nominal, real-world SO2 emissions in 2020 are much smaller than those reflected in the 2016 emission inventory. By applying the top–down adjustment described here, simulations could successfully reproduce surface SO2 concentrations, reducing RMSE by 93 % from 9.19 to 0.62 ppb. The updated SO2 and NOx emission inventories appear to successfully reproduce variations in surface PM2.5 concentrations, even after the start of LNY celebrations. However, in early February, as the impact of the COVID-19 pandemic became more significant, the baseline run (with the CREATE emission inventory) does not simulate a sudden drop in PM2.5 observations, while the adjusted emissions run does so.

A closer look, however, reveals that the real trend in PM2.5 emissions cannot be explained by the change in two major inorganic aerosol precursors: SO2 and NOx. Figure 5 depicts the time series of normalized mean biases (NMBs) of surface PM2.5 concentrations. Before LNY, PM2.5 NMB is mostly negative, showing the adjusted emission simulation slightly underestimates particulate matter. After LNY, PM2.5 NMB changes prominently, showing the simulation clearly overestimates observations by about 20 % NMB in PM2.5 concentration. Before and after LNY, PM2.5 NMB moves by 25.1 %, from -4.1 % to 21.0 %, implying that the model suddenly overestimates PM2.5 concentrations by 25 % after LNY. In other words, unknown, non-modeled emissions (that is, non-SO2 and non-NOx emissions) are clearly reduced enough during the pandemic period (February and March) to account for 25 % of total PM2.5 concentration at baseline. This result is consistent with findings (Sect. 4.1) that changes in SO2 and NOx emissions alone cannot explain the reduced PM2.5 concentrations in March.

One remaining question is why the recovery of NOx emissions and unchanged SO2 emissions at the end of March did not lead to the recovery of PM2.5, which might be explained by considering the time-varying emission contribution of each economic sector. Sensitivity tests using the CMAQ model reveal that the residential and agricultural sectors are most dominant in the early months of the year (Fig. 6), accounting for more than 60 % of surface PM2.5 concentration over China. As emissions in the residential sector are primarily from cooking and heating with anthracite coal and wood, emissions which continue even during a pandemic, one possible explanation is that emissions from the agricultural sector reduced as a result of pandemic-related delays in planting and fertilizing.

February is the start of the spring-crop planting period in southern China. The coronavirus outbreak could have impacted both field crops and livestock farms. Inputs, such as fertilizer and animal feed, have reportedly been scarce as a result of transportation disruptions, and seasonal workers have reportedly been lacking due to quarantine controls or fears (Quanying, 2020; Yu, 2020; Zhang and Xiong, 2020). Agricultural activities that generate particulate matter, such as biomass burning to clear debris and the generation of airborne dust during tilling, are reduced in intensity during the pandemic. Reduced NH3 emissions as a result of diminished livestock farming activities might also be a factor leading to lower PM2.5 concentrations.